896
The validation of numerical models is an important issue. It is particularly complex
897
in the case of field-related problems in geomorphology, where field datasets have dramatic
898
limitations, particularly in terms of spatial resolution. In addition, as models begin to
899
incorporate more and more realistic flow physics, while model verification and grid
900
independence studies are still needed (Hardy et al., 2003), validation is likely to become
901
more focussed on the details of flow physics (flow structure characterisation) rather than
902
on mean quantities. With one-dimensional and two-dimensional hydraulic models,
903
dramatic simplifications to the underlying physics are made, which means that it is
904
essential that one tests how successful such approximations are in modelling the flow. As
905
one moves to a computational fluid dynamics framework, and then through RANS, DES/LES
906
and toward direct numerical simulation of the Navier-Stokes equations, fewer
907
approximations are made, meaning that there is greater confidence that the physics are
908
appropriate. Moreover, DES/LES simulations conducted with codes that are at least second
909
order accurate in both space and time and with subgrid scale models that correctly predict
910
a zero eddy viscosity in regions where the flow is not turbulent (e.g., the dynamic
911
Smagorinsky model) and on sufficiently fine meshes especially in the wall normal direction
912
(see section 6) are likely to require less direct validation. Though a grid dependency study
913
is not required for each new application of the LES/DES code, it is highly recommended
914
such an exercise is undertaken at least one or two relevant test cases for which the relative
915
level of mesh refinement expressed in non-dimensional wall units is comparable to the one
916
used in the application of the model.
917 918
It is also important to decide what the relevant validation criteria are. Choosing the
919
vertical mean velocity profile would be meaningless for a depth-averaged two-dimensional
920
model that only yields one velocity averaged over the whole depth, but it would be
34
appropriate for three-dimensional RANS and DES/LES as capturing the secondary flow and
922
the redistribution of the streamwise momentum in the flow domain accurately is essential
923
for geosciences applications in alluvial channels where these two variables determine to a
924
large extent sediment transport and morphology changes. However, if one has chosen to
925
adopt an eddy-resolving simulation, this may be because it is expected to improve
926
estimation of mean flow parameters, but it is more likely that one wishes to extract
927
something concerning the instantaneous flow structure and dynamics of the large-scale
928
coherent structures that play an important role in bed/bank erosion and sediment
929
transport. If for example, this is the distribution of instantaneous turbulent stresses over
930
different flow quadrants, then a comparison to single-point estimates from field data may
931
still be possible (with an appropriate consideration of the scale over which flow variables
932
are averaged in time and space). If however, it is vorticity, swirling strength or similar, then
933
validation is limited by the inability to derive such quantities from field data as they require
934
simultaneous measurement of the flow at multiple neighbouring positions something
935
that is rarely possible, particularly in large channels. If the flow contains regions in which
936
well-defined large scale vortices are advected (e.g., the mixing interface at a river
937
confluence), then the peak frequencies obtained from field data velocity measurements
938
can be used for additional validation and assessment of the predictive abilities of the
939
unsteady RANS and especially DES/LES predictions. Velocity spectra measured in the field
940
can be used for additional validation. Of particular importance, is whether the DES/LES
941
simulation captures the presence of inertial -5/3 and/or of a -3 subranges. The former
942
indicates the appropriate development of the scaling regime for three-dimensional flows
943
where energy moves away from the forced scales towards the dissipative, while the latter
944
is indicative of quasi two-dimensional structures (e.g., wake of islands, mixing interfaces
945
developing in shallow channels). If these features are present in appropriate places then
946
there is some confidence that the physics at scales smaller than the largest eddies is being
947
modelled correctly.
948 949
A further consideration is the manner in which boundary conditions are input into
950
the numerical model. As Fig. 16-17 show, bed roughness induces complex flow patterns.
35
Hence, accurate modelling of flow near the bed will require high resolution bathymetry. If
952
this is not available and a RANS or eddy resolving model gives poor results near the bed, is
953
this a failure of the model, or the way in which boundary conditions have been introduced
954
into the model? Furthermore, in the field, with sediment transport potentially taking place
955
in the near-bed region, it may be difficult to locate the height of the probe above the bed,
956
and signals may decohere as suspended or bedload particles move through the
957
measurement volume. Hence, is poor agreement a necessary flaw in the model or is it
958
reflecting the complexity of undertaking precise field measurement?
959 960
Boundary conditions also include the specification of time series for each velocity
961
component for each cell at the inlet to the domain. We discussed this issue briefly at the
962
end of section 2, and Figure 18 indicates that there can be some sensitivity to the precise
963
nature of the inlet conditions, but that in areas of complex missing, such effects are
964
reduced. In this example, a precursor inlet simulation has been degraded in a controlled
965
fashion using gradual wavelet reconstruction (Keylock, 2010). When the control parameter
966
for this technique, thresh, is 1.0 the inlet conditions are identical to those from the
967
precursor simulation, when thresh = 0, the values for each velocity component time series
968
are identical to those in the precursor simulation and the Fourier spectrum is identical to
969
some error tolerance, but the correlation between time series and the nonlinearity in an
970
individual time series is destroyed. The other cases used represent intermediate conditions
971
as described by Keylock et al. (2011). It is clear from this figure that failing to correctly
972
preserve any of the correlation between time series degraded the pressure field on the
973
face and top surface of the wall-mounted rib significantly. However, in the lee of the rib,
974
there is very little difference between the simulations as the intense mixing decouples the
975
flow before and after the rib. Hence, validation of a flow field exhibits some sensitivity to
976
the nature of the inlet conditions, meaning that inlets need to be considered carefully in
977
implementation (see section 6).
978
36
Here we propose two general strategies for validation, although with applications of
980
eddy-resolving methods in geomorphology only emerging recently, a wider community
981
consensus would be needed before firm guidelines can be provided. We would suggest
982
that a two-pronged approach is useful:
983
(a) Validation using mean flow variables with a comparison to field data and, if
984
applicable, dominant frequencies of the flow in regions where large scale eddies
985
are present;
986
(b) Validation against laboratory experiments based on time-averaged and time-
987
varying parameters.
988 989
example, as shown by Kirkil and Constantinescu (2010) and Chang et al. (2011), use of
990
eddy-resolving simulations can drastically change estimates of the size of an average scour
991
zone as the resolved eddies contribute peak stresses and, thus, sediment entrainment
992
events, that remain unresolved in RANS. Hence, a comparison of mean or equilibrium
993
scour hole size between the field or experiment, and RANS and eddy-resolving simulations
994
is useful. Successful validation is also predicated on comparable spatial resolution
995
comparing a mean estimated over a computational cell that is 0.01 m3 in volume to data
996
from an ADV averaged over 1 cm3 is problematic. In this situation, if 0.01 m3 is the greatest
997
resolution attainable for reasonable computational cost, then extra thought needs to be
998
given to the density of the data collected in the field to be used in validation. In general,
999
the majority of validation variables will be derived from flow statistics. Clearly, if accurate
1000
data may be derived from multiple probes, to permit quantities such as vorticity or swirling
1001
strength to be measured directly in the field, that would be advantageous for validation.
1002
However, this is liable to be prohibitive in many situations. Hence, the recommendation
1003 1004
work, where obtaining time-varying multi-point statistics to high precision is simpler.
1005 1006
Validation should also be conceived as a multiple-step process, progressing from
1007
simple cases to the field case. That is, initial validation of the same code for simpler cases
37
for which detailed validation data exists from laboratory experiments conducted in
1009
controlled environments (e.g., under constant discharge, with well defined boundary
1010
conditions, etc.). For example in the case of a natural river confluence one expects the
1011
formation of a shallow mixing interface between the two incoming streams. It many cases,
1012
the channel curvature can be high close to the confluence region. Thus for this scenario, it
1013
is recommended the code is first validated by considering first the test case of channel flow
1014
in a curved bend and then the test case of a shallow mixing layer for which experimental
1015
data obtained at lower Reynolds numbers and in simplified channel geometries are
1016
available. Such data may include detailed vorticity and Reynolds stress measurements
1017
besides mean velocity and power spectra as well as visualizations of the instantaneous
1018
flow fields using PIV based techniques.
1019 1020
These suggestions do not resolve the question of what constitutes a validated
1021
simulation because, again, this is likely to depend on the quality, quantity and nature of
1022
variables available for validation. However, for mean flow variables, relative validation
1023
against RANS simulations is possible. If eddy-resolving methods are out-perfoming RANS
1024
methods in their representation of the mean flow field, when judged against field data,
1025
one will have some confidence that they are, at the very least, resolving the largest eddies
1026
to some accuracy, explaining the improved representation of the mean flow field. Hence,
1027
an output time series from a cell, low-pass filtered at a corresponding wavelength, is likely
1028
to be an adequate representation of the low-pass filtered equivalent processes in nature.
1029 1030
These validation issues are important as more and more DES/LES simulations are
1031
performed with commercial codes (e.g., Fluent, Flow3D) that now offer a wide choice of
1032
sub-grid scale models, time and space discretizations and mesh topologies. In many cases
1033
the users of such commercial codes have limited background knowledge in LES modelling
1034
and numerics. Thus, it is very important to consider something analogous to the validation
1035
steps articulated here before simulating a complex case with one of these codes and
1036
confidently using the data to understand the flow physics.
38 1038